Theorem biorfi 805

Description: A wff is equivalent to its disjunction with falsehood.

Hypothesis

Ref	Expression
biorfi.1	|- -. ph

Assertion

Ref	Expression
biorfi	|- (ps <-> (ps \/ ph))

Proof of Theorem biorfi

Step	Hyp	Ref	Expression
1		biorfi.1	. . 3 |- -. ph
2		biorf 804	. . 3 |- (-. ph -> (ps <-> (ph \/ ps)))
3	1, 2	ax-mp 7	. 2 |- (ps <-> (ph \/ ps))
4		orcom 264	. 2 |- ((ph \/ ps) <-> (ps \/ ph))
5	3, 4	bitri 189	1 |- (ps <-> (ps \/ ph))

Syntax hints:  -. wn 2   <-> wb 162   \/ wo 238

This theorem is referenced by:  un0 2721  opthprc 3857  imadif 4304  indifdi 13617

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 163  df-or 240  df-an 241

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